Theoretical study of some transient Couette flows of viscoelastic fluids in inertial devices

Abstract In this paper, we study three typical transient Couette flows of viscoelastic fluids when the inertia of the moving cylinders is not neglected. For these problems we give the exact velocity field as well as rigorous asymptotic expansions of the angular velocity of the inner cylinder for narrow gaps. The first study concerns the flow generated by a step change of torque imposed at the inner cylinder when the outer one is motionless. For this flow, in narrow gaps, we show that the relaxation curve of the angular velocity of the rotor in a so-called `controlled stress' device could be theoretically used to approximate the relaxation function. The second study concerns the flow generated by a step change of velocity imposed at the outer cylinder when the inner one is free to rotate and the last one concerns the flow generated when the outer cylinder is moved impulsively after which the two cylinders are free to rotate.